Chinese Quarterly Journal of Mathematics ›› 2007, Vol. 22 ›› Issue (1): 87-93.

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A Dirac Type Condition for Heavy Cycles in Weighted Graphs

  

  1. School of Mathematical Science,Shandong Normal University,Jinan 250014,China
  • Received:2003-12-23 Online:2007-03-30 Published:2023-11-15
  • About author:Ll Ping(1977-),female,native of Linyi,Shandong,an associate professor of Shandong Normal University,engages in graph theory.

Abstract: In this paper we give a Dirac type condition for heavy cycles in a 3-connected weighted graph,reading that if dw(v)≥d for all v∈V(G)\{x} and w(uz)=w(vz),when uz,vz∈E(G) and uvE(G).Then G contains either an (x,y)-cycle of weight at least 2d or a Hamilton cycle.


Key words: weighted graph, weighted degree, heavy cycle

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